\section{Extension}\label{sec:future}
Deutsch's work \cite{deutsch1962,deutsch1973} also proposed assumptions on situational trust, which reflecting the trust in different aspects of tasks. For example, I trust my brother in driving does not necessarily I trust him in flying a plane. In \cite{trust::marsh} , the whole model includes the situational trust which is made on intrinsic utility. The intrinsic utility combines risk and competent. We believe the trust model which includes situational trust can achieve better performance. For example, in viral marketing, different products can be modeled as different situations. By dedicated explicate on each seller's trust in each situation, customers can make better trust decision. We can extent our model with following notations:

\begin{table}[h]
\centering
\begin{tabular}{|p{2cm}|p{3cm}|p{2cm}|}
\hline
Description & Representation & Value Range \\ \hline
Situations & $\alpha, \beta, ...$ & \\
Societies of agents &$S_1,S_2, ... $  $S_x \in $ Set of agents  & \\
Motivation (e.g., of $\alpha$ to x at t) & $M_x(\alpha)^t$ & [0,+1] \\
Utility & $U_x(\alpha)^t$ & [-1,+1]\\
Competent & $C_x(\alpha)^t$ & 0,1\\
Risk &$U_x(\alpha)^t$ & [-1,+1)\\
Situational Trust &$T_x(y,\alpha)^t $& [-1,+1)\\
\hline
 \end{tabular}
\caption{Extension of notations for future work}
\end{table}

\subsection{Situational trust}

Situational trust is a type of interpersonal trust based on experience. Based on psychology, individuals tends to behave promotively towards things that are perceived of positive utility for them, and contriently towards negatively perceived things. Therefore, in future work, we plan to define a utility based model, which is related to:
 \begin{enumerate}
	\item strength of utility preceived;
	\item perceived increase (decrease) in likelihood of event if the the person acts promotively (contriently) to it;
	\item perceived probability of events after such promotive (contrient) behavior.
	\item intrinsic utilities of activities involved in promotive (contrient) behavior;
	\item  perceived immediacy of event's occurrence;
\end{enumerate}

There are a kind of trust different from general trust: we trust in actions rather than people. According to the Deutsch's second and fourth hypothesis \cite{trust::marsh}, motivation and utility is effected on reward or lost ($Va^-$ or $Va^+ $) to make situational trust. The utility is the expecting reward from trust. Based on Deutsch's first hypothesis \cite{trust::marsh}, it's time sensitive, $d^t$ is time discount factor:The formula is:
 \begin{equation} 
U_x(\alpha)^t=\sum{ d^tVa^+} - C\sum{d^tVa^-}
\end{equation} 
Notably, the intrinsic utility is a much more complex and wider factor that combines motivation, risk and competence. The situational trust is used to represents such balanced opinion on certain action. 
\begin{equation} 
T_x(y,\alpha)^t=U_x(\alpha)^t\times M_x(\alpha)^t \times T_x(y)^t 
\end{equation} 
However, for the rest of factors, how to make them computational is difficult. Take risk for example, according to Deutsch's research, At lease, three types of risk exist: 1. ignorance: no knowledge at all; 2. uncertainty: incomplete knowledge 3. risk: the risk based on full knowledge. Another example is motivation, which is a highly emotional concept. Admittedly, it's arguable that whether or not the whole map of trust can be a computational model. Although, with acknowledge that it's difficult to combine trust with mathematical analyses, we think the online trust is greatly a network property, a byproduct of quality of interaction between parties. Therefore, theoretically it is possible to build a computational model which captures interactions. But we do NOT intend to discuss human traits (e.g., intimate caused blind trust). Such issue may be better left for future studies. 

\subsection{Decision making based on the trust model}
Another left work is how to use our model to make decision on collaborate. The collaborate decision is also a complex process which involved more than trust. Other facts, such as competent and risk also work on it: individual would not be taking a trusting decision, rather, he would be taking a risk, or gambling. A more universal trust model needs to include them for more accurate collaborate decision. 